Convergence of Proximal Gradient Algorithm in the Presence of Adjoint Mismatch

  • Émilie Chouzenoux
  • Jean-Christophe Pesquet
  • Cyril Riddel
  • Marion Savanier
  • Yves Trousset
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , , , , ,

    We consider the proximal gradient algorithm for solving penalized least-squares minimization problems arising in data science. This first-order algorithm is attractive due to its flexibility and minimal memory requirements allowing to tackle large-scale minimization problems involving non-smooth penalties. However, for problems such as X-ray computed tomography, the applicability of the algorithm is dominated by the … Read more

    Robot Dance: a mathematical optimization platform for intervention against Covid-19 in a complex network

  • Luis Gustavo Nonato
  • Claudia Sagastizábal
  • Paulo J. S. Silva
  • Pedro Peixoto
  • Tiago Pereira
    • Categories Biomedical Applications Tags , , ,

    Robot Dance is a computational platform developed in response to the coronavirus outbreak, to support the decision making on public policies at a regional level. The tool is suitable for understanding and suggesting levels of intervention needed to contain the spread of diseases when the mobility of inhabitants through a regional network is a concern. … Read more

    Tight bounds on the maximal perimeter and the maximal width of convex small polygons

  • Christian Bingane
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Quadratic Programming Tags , , , , ,

    A small polygon is a polygon of unit diameter. The maximal perimeter and the maximal width of a convex small polygon with $n=2^s$ vertices are not known when $s \ge 4$. In this paper, we construct a family of convex small $n$-gons, $n=2^s$ and $s\ge 3$, and show that the perimeters and the widths obtained … Read more

    Optimization with Least Constraint Violation

  • Yu-Hong Dai
  • Liwei Zhang
    • Categories Nonlinear Optimization Tags , , , ,

    Study about theory and algorithms for constrained optimization usually assumes that the feasible region of the optimization problem is nonempty. However, there are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constraint violation prefer to be found. A … Read more

    Improved Branch-and-Cut for the Inventory Routing Problem Based on a Two-Commodity Flow Formulation

  • Eleftherios G. Manousakis
  • Panagiotis P. Repoussis
  • Christos D. Tarantilis
  • Emmanouil Zachariadis
    • Categories Branch and Cut Algorithms, Supply Chain Management

    This paper examines the Inventory Routing Problem (IRP) with Maximum Level inventory policy. The IRP is a broad class of hard to solve problems with numerous practical applications in the field of freight transportation and logistics. A supplier is responsible for determining the timing and the quantity of replenishment services offered to a set of … Read more

    New efficient approach in finding a zero of a maximal monotone operator

  • Ba Khiet Le
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , ,

    In the paper, we provide a new efficient approach to find a zero of a maximal monotone operator under very mild assumptions. Using a regularization technique and the proximal point algorithm, we can construct a sequence that converges strongly to a solution with at least linear convergence rate. Article Download View New efficient approach in … Read more

    Optimal Steiner Trees Under Node and Edge Privacy Conflicts

  • Roberto Baldacci
  • Alessandro Hill
  • Stefan Voss
    • Categories Branch and Cut Algorithms, Network Optimization, Telecommunications Tags , , , ,

    In this work, we suggest concepts and solution methodologies for a series of strategic network design problems that find application in highly data-sensitive industries, such as, for instance, the high-tech, governmental, or military sector. Our focus is on the installation of widely used cost-efficient tree-structured communication infrastructure. As base model we use the well-known Steiner … Read more

    Optimizing hypergraph-based polynomials modeling job-occupancy in queueing with redundancy scheduling

  • Daniel Brosch
  • Monique Laurent
  • Andries Steenkamp
    • Categories Constrained Nonlinear Optimization Tags , , ,

    We investigate two classes of multivariate polynomials with variables indexed by the edges of a uniform hypergraph and coefficients depending on certain patterns of union of edges. These polynomials arise naturally to model job-occupancy in some queuing problems with redundancy scheduling policy. The question, posed by Cardinaels, Borstand van Leeuwaarden (arXiv:2005.14566, 2020), is to decide … Read more

    Generalized Self-Concordant Analysis of Frank-Wolfe algorithms

  • Pavel Dvurechensky
  • Shimrit Shtern
  • Kamil Safin
  • Mathias Staudigl
    • Categories Convex Optimization

    Projection-free optimization via different variants of the Frank-Wolfe (FW) method has become one of the cornerstones in large scale optimization for machine learning and computational statistics. Numerous applications within these fields involve the minimization of functions with self-concordance like properties. Such generalized self-concordant (GSC) functions do not necessarily feature a Lipschitz continuous gradient, nor are … Read more

    Risk-Averse Multistage Stochastic Programs with Expected Conditional Risk Measures

  • Maryam Khatami
  • Lewis Ntaimo
  • Bernardo K. Pagnoncelli
  • Thuener Silva
    • Categories Stochastic Programming Tags , ,

    We study decomposition algorithms for risk-averse multistage stochastic programs with expected conditional risk measures (ECRMs). ECRMs are attractive because they are time-consistent, which means that a plan made today will not be changed in the future if the problem is re-solved given a realization of the random variables. We show that solving risk-averse problems based … Read more